q-Fock Space Representations of the q-Lorentz Algebra and Irreducible Tensors

Abstract

We present the q-deformation of the Lorentz algebra, with Hopf structure, in terms of four independent harmonic oscillators. The explicit realization of the q-Fock space is given and the irreducible finite-dimensional representations of so(1,3)q are described and characterized by its two q-Casimir operators. The concept of irreducible q-Lorentz tensor is also introduced. The analysis is made for a real deformation parameter.